Advanced imaging technologies, such as microscopy and spectroscopy, have often been employed by scientists and engineers to gain insights into materials of interest. Such technologies provide a two (or higher) dimensional magnified image of the material (or at least a part thereof). Analysis techniques may then be applied on the acquired image to visualize the internal structure and/or to characterize the material. Depending on the analysis, a number of characteristic properties are measured and quantified, such as structure, type and number of distinct phases, phase morphology, and phase chemistry.
Regardless of the characteristic properties being measured, it is recognized that a majority of natural and man-made materials possess a high degree of heterogeneity, often as the result of varying voids and grain sizes. Such heterogeneity often makes it challenging to find a suitable sample volume that, for the purposes of engineering analysis, may be regarded as representative of the material body as a whole. Typically, the smallest such volume (or, in the case of a two dimensional image, the smallest such area) is called the representative elementary volume (“REV”).
There are a number of existing REV determination procedures, at least one of which performs adequately for relatively homogenous materials. See, e.g., Costanza-Robinson, et al. “REV estimation for porosity, moisture saturation, and air-water interfacial areas in unsaturated porous media: Data quality implications”, Water Resources Research, v47, W07513, 2011. Nevertheless, existing methods may suffer from a number of shortcomings, including overestimation, overly-generous search region requirements, overly-restrictive subsample positioning requirements, and a general inability to cope with relatively heterogeneous materials.